Question

1. if the figure below is a regular polygon, find the value of x.

(10x + 4)°

Explanation:

Step1: Determine the number of sides

The polygon in the figure is a nonagon (9 - sided polygon).

Step2: Recall the formula for interior angle of regular polygon

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \). For \( n = 9 \), we have:

$$ \frac{(9 - 2)\times180^{\circ}}{9}=\frac{7\times180^{\circ}}{9}=140^{\circ} $$

Step3: Set up the equation

We know that each interior angle is \( (10x + 4)^{\circ} \), so we set up the equation:

$$ 10x + 4 = 140 $$

Step4: Solve for \( x \)

Subtract 4 from both sides:

$$ 10x = 140 - 4 = 136 $$

Divide both sides by 10:

$$ x=\frac{136}{10}=13.6 $$

Answer:

\( x = 13.6 \)